scholarly journals Acceleration phase and improved rocket model for indirectly driven capsules

2004 ◽  
Vol 22 (4) ◽  
pp. 451-459 ◽  
Author(s):  
YVES SAILLARD
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Maximum Temperature ◽  
System Of Differential Equations ◽  
Acceleration Phase ◽  
Conservation Principles ◽  
Ablation Pressure ◽  
Two Phases ◽  
Ablated Mass

The system of differential equations for the non-ablated mass, the average implosion velocity, and the ablation radius of an indirectly driven capsule in acceleration phase, has been obtained from conservation principles of hydrodynamics. Two phases are distinguished during acceleration, according to the uniformity of the velocity in the non-ablated shell. The results of the integration of this system are well compared with numerical simulation of optimized capsules. Assuming that the ablation pressure depends only on the Hohlraum temperature, the relations between the non-ablated mass, the implosion velocity, and the ablation radius are obtained for optimized temperature shape. These relations provide the maximum implosion velocity and the remaining non-ablated mass in terms of the initial capsule and the maximum temperature (or the initial capsule mass in terms of the remaining non-ablated mass) useful to determine the required ablator thickness for optimized capsules. These results are also compared with numerical simulations of different capsules.

Numerical vs. Experimental Predictions of Yaw Motion of Single Point Moored Vessel

2005 ◽  
Author(s):  
Mathieu Brotons ◽  
Philippe Jean
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Time Domain ◽  
Model Tests ◽  
Linear Differential Equations ◽  
Integration Scheme ◽  
Engineering Model ◽  
Non Linear ◽  
Linear Differential

The accurate prediction of SPM vessel yaw motion is important to its mooring system design. Inconsistencies have been observed between the numerical and model test predictions of offloading responses. In some cases, the numerical simulation predicted unstable yaw behavior of the vessel (fishtailing) while the model tests did not show such instability. This discrepancy between experiment and theory casts doubt as to whether the numerical simulation predicts correctly the vessel yaw motion. The work presented in this paper investigates the following two hypotheses to possibly explain the non-expected fishtailing in the numerical simulations: The mooring software may not accurately integrate non-linear differential equations that describe the yaw motion of the SPM vessel. Some damping terms may be under-estimated in the software (user input issue). To validate the integration scheme of the system of non-linear differential equations as implemented in the mooring software, a stability analysis has been conducted on a shuttle tanker moored to a West Africa deep water buoy. Variations of parameters like the hawser length, its axial stiffness and the vessel’s drag coefficients have been studied to explore their impacts on the vessel yaw stability. The approach is to identify without performing any time domain simulations, the domains of stability by linearizing the differential equations of SPM vessel’s yaw motion around its equilibrium point. The validity of the developed approach is then confirmed by performing time domain simulations of the same case. The second conjecture which may explain the non-expected fishtailing in numerical simulations was that some damping terms may be under-estimated. A semi empirical formula for the drag moment can be derived from rotation tests and comparisons were performed with the engineering model implemented in the mooring analysis software. The results show that by calibrating this damping term with the one derived from the experiments, the numerical simulations would match the stable yaw motion behavior as predicted during model tests. Following the above findings, a tool has been developed to fit the yaw drag moment engineering model based on experimental measurements, for any case of mooring analysis.

scholarly journals A Study on the Complexity of a New Chaotic Financial System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Yi Liao ◽  
Yiran Zhou ◽  
Fei Xu ◽  
Xiao-Bao Shu
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Financial System ◽  
System Of Differential Equations ◽  
Bifurcation Diagrams ◽  
Complex Dynamic ◽  
System Parameters ◽  
Wide Range

The interaction of elements in a financial system can exhibit complex dynamic behaviours. In this article, we use a system of differential equations to model the evolution of a financial system and study its complexity. Numerical simulations show that the system exhibits a variety of rich dynamic behaviours, including chaos. Bifurcation diagrams show that the system behaves chaotically over a wide range of system parameters.

scholarly journals MODEL MATEMATIKA KEARIFAN LOKAL MASYARAKATDESA TRUSMI DALAM MENJAGA EKSISTENSIKERAJINAN BATIK TULIS

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Arif Muchyidin
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Numerical Simulation ◽  
National Identity ◽  
Differential Equations ◽  
Critical Point ◽  
Critical Points ◽  
System Of Differential Equations ◽  
The Stability ◽  
The Village

Batik as an Indonesian national identity has contributed greatly to the Indonesian economy. However, the value of exports and other economic potentials are not supported by the number of batik, especially batik artisans in the village Trusmi. Trusmi batik artisans in the village is a craftsman who has been there all the time and remain there for generations. The phenomenon that occurs in the craft of batik Trusmi analyzed with mathematical modeling approach, in this case the dynamical system. From the resulting system of differential equations, then analyzed the stability around the critical point. From the resulting model, gained two critical points. The first critical point is a condition where there is no proficient craftmen (not expected), whereas at the second critical point is the potential of batik craftmen and proficient craftmen mutually exist, or in other words batik will still exist. From the results of numerical simulation, if , then batik Trusmi will still exist. However, if , then the number of proficient craftmen would quickly dwindle and slowly batik will be extinct.Key Words : dinamical system, critical points, stability

scholarly journals Modeling Separation Process for Sunflower Seed Mixture on Vibro-Pneumatic Separators

Mechanika ◽  
2021 ◽  
Vol 27 (4) ◽  
pp. 311-320
Author(s):  
Igor SHEVCHENKO ◽  
Elchyn ALIIEV ◽  
Gintas VISELGA ◽  
Jan Radek KAMINSKI
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Sunflower Seed ◽  
Oscillation Amplitude ◽  
Effective Diameter ◽  
Sunflower Seeds ◽  
System Of Differential Equations ◽  
Seed Supply ◽  
Granular Gas ◽  
Seed Mixture

Aim of the research is to increase the efficiency of the mechanical and technological process of separation of sunflower seed mixture on vibro-pneumatic separators, the principle of which is based on the interaction of seed flow with the surface having fluctuation-type vibration load by substantiating their efficient processing and technological parameters. A system of differential equations of sunflower seeds motions, as a granular gas, under the action of a vibrating surface was developed, taking into account the elastic-damping interaction and physical and mechanical properties of seeds. The presented system of differential equations is the basis of the physical and mathematical means of numerical modeling of this process, which was implemented in the software package STAR-CCM +. To build physical and mathematical models, it was assumed that sunflower seeds are presented in the form of ellipsoids with a certain density and effective diameter. As a result of numerical simulation of the process of moving sunflower seeds under the action of a vibrating sieve, dependences of the change in total concentration θ and productivity q on seed supply Q, sieve angle α, sieve frequency ψ and sieve amplitude A were obtained. As a result of numerical simulation of the process of moving sunflower seeds under the action of a vibrating surface, dependences of the change of filling factor χ, distribution coefficient δ and productivity q on seed supply Q, vibration surface angles α and β, oscillation frequency ψ, oscillation amplitude A and set air velocity V were obtained. Theoretical provisions were implemented and tested in the development of an adaptive vibrating screen separator of sunflower seeds (Ukrainian patent #120235).

A New Method to Find the Base Functions for the Method of Directly Defining the Inverse Mapping (MDDiM)

2018 ◽  
Vol 09 (04) ◽  
pp. 1850008
Author(s):  
OPhir Nave
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Analytical Solution ◽  
Differential Equations ◽  
Analytical Solutions ◽  
New Method ◽  
Fuel Spray ◽  
System Of Differential Equations ◽  
Inverse Mapping ◽  
Base Functions

In this paper, we apply a new algorithm called method of directly defining the inverse mapping (MDDiM) that was introduced by Liao for finding a semi-analytical solution to nonlinear system of differential equations. We apply this new method to the autoignition of a monodisperse fuel spray model. We use this technique for finding the base functions in the considered algorithm. Our results include a comparison between a numerical simulation and an analytical solutions derived from the MDDiM.

scholarly journals MODEL MATEMATIKA KEARIFAN LOKAL MASYARAKATDESA TRUSMI DALAM MENJAGA EKSISTENSIKERAJINAN BATIK TULIS

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Arif Muchyidin
Keyword(s):  
Mathematical Modeling ◽  
Dynamical System ◽  
Numerical Simulation ◽  
National Identity ◽  
Differential Equations ◽  
Critical Point ◽  
Critical Points ◽  
System Of Differential Equations ◽  
The Stability ◽  
The Village

Batik as an Indonesian national identity has contributed greatly to the Indonesian economy. However, the value of exports and other economic potentials are not supported by the number of batik, especially batik artisans in the village Trusmi. Trusmi batik artisans in the village is a craftsman who has been there all the time and remain there for generations. The phenomenon that occurs in the craft of batik Trusmi analyzed with mathematical modeling approach, in this case the dynamical system. From the resulting system of differential equations, then analyzed the stability around the critical point. From the resulting model, gained two critical points. The first critical point is a condition where there is no proficient craftmen (not expected), whereas at the second critical point is the potential of batik craftmen and proficient craftmen mutually exist, or in other words batik will still exist. From the results of numerical simulation, if , then batik Trusmi will still exist. However, if , then the number of proficient craftmen would quickly dwindle and slowly batik will be extinct.Key Words : dinamical system, critical points, stability

NUMERICAL SIMULATION OF TWO-PHASES FLOW ON PUMPS INLET SYSTEM FOR SHALLOW WATER

2019 ◽  
Author(s):  
Livio Sebastián Maglione ◽  
Guillermo Muschiatto ◽  
Raúl Alberto DEAN
Keyword(s):  
Numerical Simulation ◽  
Shallow Water ◽  
Inlet System ◽  
Two Phases ◽  
Two Phases Flow
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